Hypothesis Testing: Playbill Magazine

In 2010, Playbill Magazine contacted Boos Allen to determine the mean annual household income of its readers. Using a list of customers provided by Playbill, Boos Allen randomly sampled 300 Playbill customers. From that sample, Boos Allen is confident that the population average Playbill reader's household income is $119,155, and has a population sample household income standard deviation of $30,000.

Recently two Playbill executives suggested that Playbill's reader mean average household income has increased and the magazine price should be raised. As Playbill's new marketing manager, you convince Playbill's chief operating officer to complete a second survey with Boos Allen to confirm that assertion. Yesterday the new Boos Allen report appeared on your desk. From another sample of Playbill customers taken from a recent list of customers you e-mailed Boos Allen, the 2012 Playbill customer's profile is a mean annual household income of $124,450 with a population standard deviation of household income unchanged at $30,000.

Now answer the following below
- What is the null hypothesis-both explanation and math equation?
- what is the alternative hypothesis -both explanation and math equation?
- Solve the equation. Would you accept or reject null hypothesis?
-Does the p-value indicate acceptance or rejection of the null using alpha is .05?
- Why why you can be statistically confident that the average amount a food court's customer spends has increased, decreased, or remains the same, and what would happen if alpha was .01 or .10?

Attachments

Solution Preview

I have attached a Word document with a detailed solution. I have also attached a copy of your Excel sheet. There were errors on the sheet for testing a hypothesis about a mean with sigma known, particularly the p-values for the single tail alternatives were reversed. I have corrected the error and highlighted the correct p-value for this problem in green.

Given the following case scenario:

In 2010, Playbill Magazine contacted Boos Allen to determine the mean annual household income of its readers. Using a list of customers provided by Playbill, Boos Allen randomly sampled 300 Playbill customers. From that sample, Boos Allen is confident that the population average Playbill reader's household income is $119,155, and has a population sample household income standard deviation of $30,000.

Recently two Playbill executives suggested that Playbill's reader mean average household income has increased and the magazine price should be raised. As Playbill's new marketing manager, you convince Playbill's chief operating officer to ...